On a conjecture of Le Bruyn
Anne Cortella, Boris Kunyavskii
math.AGarXiv:math/9803103
Abstract
Given a generic field extension F/k of degree n>3 (i.e. the Galois group of the normal closure of F is isomorphic to the symmetric group Sn), we prove that the norm torus, defined as the kernel of the norm map N:RF/k(Gm)m, is not rational over k.
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